Meenakshy Jyothis
University of Oklahoma
Title
Stars at infinity in the Thurston boundary
Abstract
For a complete metric space with a chosen compactification, the star of a boundary point is a subset of the boundary determined by the metric and the compactification. Karlsson introduced stars to study the dynamics of isometries. For instance, under suitable hypotheses, iterates of an isometry carry points outside the repelling based star toward the attracting based star, giving a generalized north–south behavior. In this talk, we study stars in the Thurston compactification of Teichmüller space with respect to Thurston’s metric and the Teichmüller metric. We show that the stars for these metrics differ, disproving Karlsson’s conjecture for the Teichmüller metric. For surfaces of complexity at least two, we show that the hyperbolic boundary points for both metrics are precisely the projective classes of uniquely ergodic measured laminations. This is joint work with Jing Tao.
